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.\"     from: @(#)hypot.3	6.7 (Berkeley) 5/6/91
.\"	$NetBSD: hypot.3,v 1.17 2007/02/22 22:08:20 drochner Exp $
.\"
.Dd February 12, 2007
.Dt HYPOT 3
.Os
.Sh NAME
.Nm hypot ,
.Nm hypotf
.Nd Euclidean distance and complex absolute value functions
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn hypot "double x" "double y"
.Ft float
.Fn hypotf "float x" "float y"
.Sh DESCRIPTION
The
.Fn hypot
functions
compute the
sqrt(x*x+y*y)
in such a way that underflow will not happen, and overflow
occurs only if the final result deserves it.
.Pp
.Fn hypot "\*(If" "v"
=
.Fn hypot "v" "\*(If"
= +\*(If for all
.Ar v ,
including \*(Na.
.Sh ERRORS
Below 0.97
.Em ulps .
Consequently
.Fn hypot "5.0" "12.0"
= 13.0
exactly;
in general, hypot returns an integer whenever an
integer might be expected.
.Pp
The same cannot be said for the shorter and faster version of hypot
that is provided in the comments in cabs.c; its error can
exceed 1.2
.Em ulps .
.Sh NOTES
As might be expected,
.Fn hypot "v" "\*(Na"
and
.Fn hypot "\*(Na" "v"
are \*(Na for all
.Em finite
.Ar v ;
with "reserved operand" in place of "\*(Na", the
same is true on a
.Tn VAX .
But programmers on machines other than a
.Tn VAX
(it has no \*(If)
might be surprised at first to discover that
.Fn hypot "\(+-\*(If" "\*(Na"
= +\*(If.
This is intentional; it happens because
.Fn hypot "\*(If" "v"
= +\*(If
for
.Em all
.Ar v ,
finite or infinite.
Hence
.Fn hypot "\*(If" "v"
is independent of
.Ar v .
Unlike the reserved operand fault on a
.Tn VAX ,
the
.Tn IEEE
\*(Na is designed to
disappear when it turns out to be irrelevant, as it does in
.Fn hypot "\*(If" "\*(Na" .
.Sh SEE ALSO
.Xr math 3 ,
.Xr sqrt 3
.Sh HISTORY
Both a
.Fn hypot
function and a
.Fn cabs
function
appeared in
.At v7 .
.Fn cabs
was removed from public namespace in
.Nx 5.0
to avoid conflicts with the complex function in C99.
